baptized in Jesus's name

A non-catholic friend of mine told me that I needed to be baptized in Jesus’s name not the Father, Son and Holy Spirit. I did not say anything because I did not know why we baptized in the Father, Son and Holy Spirit and could not defend our ways. I did research and found that Peter did say to the Jews “Repent and be baptized, every one of you, in the name of Jesus Christ…” Can you please tell me why we baptize in the Father, Son and Holy Spirit so I can tell my non-catholic friend.

Jesus said, “Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit” (Mt. 28:19). When Peter said "Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins” (Acts 2:38) he was not dictating a formula. A Catholic Commentary on Holy Scripture explains, “baptism in the name of Jesus is not a liturgical formula but distinguishes Christian baptism from… that of John the Baptist… or that given to proselytes.”

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